Core-periphery structure is an essential mesoscale feature in complex networks. Previous researches mostly focus on discriminative approaches while in this work, we propose a generative model called masked Bayesian non-negative matrix factorization. We build the model using two pair affiliation matrices to indicate core-periphery pair associations and using a mask matrix to highlight connections to core nodes. We propose an approach to infer the model parameters, and prove the convergence of variables with our approach. Besides the abilities as traditional approaches, it is able to identify core scores with overlapping core-periphery pairs. We verify the effectiveness of our method using randomly generated networks and real-world networks. Experimental results demonstrate that the proposed method outperforms traditional approaches.